Euler Products And Eisenstein Series

Author : Gorō Shimura
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 44,5 Mb
Release : 1997
Category : Eisenstein series
ISBN : 9780821805749

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Euler Products and Eisenstein Series by Gorō Shimura Pdf

This volume has three chief objectives: 1) the determination of local Euler factors on classical groups in an explicit rational form; 2) Euler products and Eisenstein series on a unitary group of an arbitrary signature; and 3) a class number formula for a totally definite hermitian form. Though these are new results that have never before been published, Shimura starts with a quite general setting. He includes many topics of an expository nature so that the book can be viewed as an introduction to the theory of automorphic forms of several variables, Hecke theory in particular. Eventually, the exposition is specialized to unitary groups, but they are treated as a model case so that the reader can easily formulate the corresponding facts for other groups. There are various facts on algebraic groups and their localizations that are standard but were proved in some old papers or just called well-known. In this book, the reader will find the proofs of many of them, as well as systematic expositions of the topics. This is the first book in which the Hecke theory of a general (nonsplit) classical group is treated. The book is practically self-contained, except that familiarity with algebraic number theory is assumed.

Author : Gorō Shimura
Publisher : American Mathematical Soc.
Page : 284 pages
File Size : 52,9 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 0821889370

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Euler Products and Eisenstein Series by Gorō Shimura Pdf

This volume has three chief objectives: 1) the determination of local Euler factors on classical groups in an explicit rational form; 2) Euler products and Eisenstein sereis on a unitary group of an arbitrary signature; and 3) a class number formula for a totally definite hermitian form. Though these are new results that have never before been published, Shimura starts with a quite general setting. He includes many topics of an expository nature so that the book can be viewed as an introduction to the theory of automorphic forms of several variables, Hecke theory in particular. Eventually, the exposition is specialized to unitary groups, but they are treated as a model case so that the reader can easily formulate the corresponding facts for other groups. There are various facts on algebraic groups and their localiztions that are standard but were proved in some old papers or just called "well-known". In this book, the reader will find the proofs of many of them, as well as systematic expositions of the topics. This is the first book in which the Hecke theory of a general (nonsplit) classical group is treated. The book is practically self-contained, except that familiarity with algebraic number theory is assumed.

Author : Robert S. Doran
Publisher : American Mathematical Soc.
Page : 293 pages
File Size : 53,5 Mb
Release : 1999
Category : Electronic
ISBN : 9780821810507

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Automorphic Forms, Automorphic Representations, and Arithmetic by Robert S. Doran Pdf

Author : Robert S. Doran
Publisher : Oxford University Press, USA
Page : 304 pages
File Size : 55,8 Mb
Release : 1999
Category : Mathematics
ISBN : UCSC:32106015382861

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Automorphic Forms, Automorphic Representations, and Arithmetic by Robert S. Doran Pdf

Professor Goro Shimura was principal speaker at the conference on "Euler Products and Eisenstein Series" held at Texas Christian University (See CBMS Regional Conference Series in Mathematics, Volume 93). The present volume contains articles by leading specialists in the field. Some of these articles are based on talks given at the conference, whereas others were written purposely for this volume. The variety of the work presented reflects the current active state of thetopic.

Author : Goro Shimura
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 47,5 Mb
Release : 2014-05-27
Category : Education
ISBN : 9781470415624

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Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups by Goro Shimura Pdf

In this book, award-winning author Goro Shimura treats new areas and presents relevant expository material in a clear and readable style. Topics include Witt's theorem and the Hasse principle on quadratic forms, algebraic theory of Clifford algebras, spin groups, and spin representations. He also includes some basic results not readily found elsewhere. The two principle themes are: (1) Quadratic Diophantine equations; (2) Euler products and Eisenstein series on orthogonal groups and Clifford groups. The starting point of the first theme is the result of Gauss that the number of primitive representations of an integer as the sum of three squares is essentially the class number of primitive binary quadratic forms. Presented are a generalization of this fact for arbitrary quadratic forms over algebraic number fields and various applications. For the second theme, the author proves the existence of the meromorphic continuation of a Euler product associated with a Hecke eigenform on a Clifford or an orthogonal group. The same is done for an Eisenstein series on such a group. Beyond familiarity with algebraic number theory, the book is mostly self-contained. Several standard facts are stated with references for detailed proofs. Goro Shimura won the 1996 Steele Prize for Lifetime Achievement for "his important and extensive work on arithmetical geometry and automorphic forms".

Author : Henryk Iwaniec
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 41,6 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821807774

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Topics in Classical Automorphic Forms by Henryk Iwaniec Pdf

This volume discusses various perspectives of the theory of automorphic forms drawn from the author's notes from a Rutgers University graduate course. In addition to detailed and often nonstandard treatment of familiar theoretical topics, the author also gives special attention to such subjects as theta- functions and representatives by quadratic forms. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Thanasis Bouganis,Otmar Venjakob
Publisher : Springer
Page : 483 pages
File Size : 43,9 Mb
Release : 2014-12-08
Category : Mathematics
ISBN : 9783642552458

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Iwasawa Theory 2012 by Thanasis Bouganis,Otmar Venjakob Pdf

This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida’s theory of p-adic modular forms and big Galois representations play a crucial part. Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan).

Author : Robert S. Doran
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 53,8 Mb
Release : 1999
Category : Electronic
ISBN : 9780821810514

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Automorphic Forms, Automorphic Representations, and Arithmetic by Robert S. Doran Pdf

Author : Wee Teck Gan,Stephen S. Kudla,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 46,8 Mb
Release : 2007-12-22
Category : Mathematics
ISBN : 9780817646394

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Eisenstein Series and Applications by Wee Teck Gan,Stephen S. Kudla,Yuri Tschinkel Pdf

Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.

Author : Goro Shimura
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 49,8 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821849613

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Arithmeticity in the Theory of Automorphic Forms by Goro Shimura Pdf

Written by one of the leading experts, venerable grandmasters, and most active contributors $\ldots$ in the arithmetic theory of automorphic forms $\ldots$ the new material included here is mainly the outcome of his extensive work $\ldots$ over the last eight years $\ldots$ a very careful, detailed introduction to the subject $\ldots$ this monograph is an important, comprehensively written and profound treatise on some recent achievements in the theory. --Zentralblatt MATH The main objects of study in this book are Eisenstein series and zeta functions associated with Hecke eigenforms on symplectic and unitary groups. After preliminaries--including a section, ``Notation and Terminology''--the first part of the book deals with automorphic forms on such groups. In particular, their rationality over a number field is defined and discussed in connection with the group action; also the reciprocity law for the values of automorphic functions at CM-points is proved. Next, certain differential operators that raise the weight are investigated in higher dimension. The notion of nearly holomorphic functions is introduced, and their arithmeticity is defined. As applications of these, the arithmeticity of the critical values of zeta functions and Eisenstein series is proved. Though the arithmeticity is given as the ultimate main result, the book discusses many basic problems that arise in number-theoretical investigations of automorphic forms but that cannot be found in expository forms. Examples of this include the space of automorphic forms spanned by cusp forms and certain Eisenstein series, transformation formulas of theta series, estimate of the Fourier coefficients of modular forms, and modular forms of half-integral weight. All these are treated in higher-dimensional cases. The volume concludes with an Appendix and an Index. The book will be of interest to graduate students and researchers in the field of zeta functions and modular forms.

Author : Goro Shimura
Publisher : Springer Science & Business Media
Page : 820 pages
File Size : 52,8 Mb
Release : 2002-09-10
Category : Mathematics
ISBN : 0387954066

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Collected Papers I by Goro Shimura Pdf

In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement :" To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field.." 103 of Shimura ́s most important papers are collected in four volumes. Volume I contains his mathematical papers from 1954 to 1966 and some notes to the articles.

Author : Goro Shimura
Publisher : Springer Science & Business Media
Page : 856 pages
File Size : 42,6 Mb
Release : 2002-12-06
Category : Mathematics
ISBN : 0387954163

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Collected Papers II by Goro Shimura Pdf

In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement :" To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field." 103 of Shimura ́s most important papers are collected in four volumes. Volume II contains his mathematical papers from 1967 to 1977 and some notes to the articles.

Author : Goro Shimura
Publisher : Springer Science & Business Media
Page : 922 pages
File Size : 48,5 Mb
Release : 2002-10-31
Category : Mathematics
ISBN : 0387954171

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Collected Papers III by Goro Shimura Pdf

In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement :" To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field." 103 of Shimura ́s most important papers are collected in four volumes. Volume III contains his mathematical papers from 1978 to 1988 and some notes to the articles.

Author : Haruzo Hida
Publisher : Cambridge University Press
Page : 404 pages
File Size : 51,7 Mb
Release : 1993-02-11
Category : Mathematics
ISBN : 0521435692

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Elementary Theory of L-functions and Eisenstein Series by Haruzo Hida Pdf

The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.

Author : Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 44,5 Mb
Release : 2007-10-10
Category : Mathematics
ISBN : 9780817646462

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Representation Theory and Automorphic Forms by Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang Pdf

This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.